Two-dimensional nuclear magnetic resonance spectrometry

ABSTRACT

A two-dimensional nuclear magnetic resonance spectrometry which comprises the following steps to facilitate phase correction: 
     (a) taking the Fourier transform of the set S(t 1 , t 2 ) of the free induction decay signals with respect to t 2  to generate the transformed data sets of S c  (t 1 , F 1 ) or S s  (t 1 , F 2 ), the signals being stored in the memory corresponding to the values of t 1  ; 
     (b) obtaining data S c  (t 1000 , F 2 ) and S s  (t 1000 , F 2 ) whose phases have been shifted by phase angle θ 2 , from the initial data S c  (t 1000 , F 2 ) and S s  (t 1000 , F 2 ) contained in two Fourier components S c  (t 1 , F 2 ) and S s  (t 1 , F 2 ) derived by the Fourier transformation made in the step (a), in such a way that the peak contained in the initial data S c  (t 1000 , F 2 ) and S s  (t 1000 , F 2 ) takes an absorption or dispersion waveform to make phase correction; 
     (c) shifting the phases of the data in the data sets S c  (t 1 , F 2 ) or S s  (t 1 , F 2 ) derived in the step (b) by phase angle θ 1  to make phase correction with respect to t 1  ; and 
     (d) taking the Fourier transform of the data sets S c  (t 1 , F 2 ) or S s  (t 1 , F 2 ) with respect to t 1 .

RELATED APPLICATION

This application is a continuation-in-part of U.S. application Ser. No.732,846, filed May 10, 1985, now U.S. Pat. No. 4,677,383.

BACKGROUND OF THE INVENTION

The present invention relates to a two-dimensional nuclear magneticresonance spectrometry and, more particularly, to a two-dimensionalnuclear magnetic resonance spectrometry that can offer two-dimensionalspectra whose phases have been corrected.

In recent years, two-dimensional nuclear magnetic resonance spectrometryhas attracted special interest as a new NMR spectrometry. According tothis spectrometry (the spectrometry specified by W. P. Aue, E.Bartholdi, and R. R. Ernst in "Two-dimensional spectroscopy. Applicationto nuclear magnetic resonance," Journal of Chemical Physics, Vol. 64,No. 5, Mar. 1, 1976, pp. 2229-2246), NMR signals are represented as atwo-dimensional spectrum, and therefore it yields higher resolution thanthe prior art method, i.e., a resonance line is better split intomultiplet lines. This facilitates analyzing spectra and so thespectrometry is expected to find much wider application in the future.

FIG. 1 shows a sequence of measurements made for J-resolvedtwo-dimensional NMR which is one of the two-dimensional NMRs.Specifically, a 90° pulse and a 180° pulse are applied at a timeinterval of t₁ /2 to a sample containing gyromagnetic resonators. Afterthe lapse of t₁ /2, the resulting free induction decay signal isdetected for a period t₂ and stored in a memory. This one measurement isrepeated many times with incrementally different values of t₁. The freeinduction decay signals which are obtained by these measurements arestored in the memory, corresponding to the values of t₁. Then, the setS(t₁, t₂) of the signals are subjected to double Fourier transformationwith respect to t₂ and t₁ to derive a two-dimensional spectrum.

In this two-dimensional NMR spectrometry, it is difficult to correct thephase of the obtained two-dimensional spectrum. Therefore, the spectrumis derived as a power spectrum that is independent of phase. In a powerspectrum, any peak terminates in a tail. Near such a tail resonancelines cannot be well separated. In an attempt to maximize the separationfree induction decay signals have been heretofore multiplied by variouswindow functions. However, complete separation has been impossible torealize. Further, the multiplications using window functions pose theadditional problem that peaks vanish.

SUMMARY OF THE INVENTION

In view of the foregoing problems, it is the main object of the presentinvention to provide a two-dimensional nuclear magnetic resonancespectrometry in which the phases of two-dimensional spectra can beeasily corrected.

This object is achieved in accordance with the teachings of the presentinvention by a two-dimensional nuclear magnetic resonance spectrometrycomprising the steps of:

(a) applying a radio-frequency pulse train to a sample containinggyromagnetic resonators, the pulse train consisting of a plurality ofradio-frequency pulses;

(b) detecting the free induction decay after the end of the applicationof the radio-frequency pulse train and storing it in a memory;

(c) repeating the steps (a) and (b) with different values of evolutionperiod t₁ that is defined as the pulse separation between certain twopulses of the radio-frequency pulse train to generate the data set S(t₁,t₂) of the free induction decay signals, the initial value of t₁ beingidentified as t₁₀₀₀ ;

(d) taking the Fourier transform of the set S(t₁, t₂) of the freeinduction decay signals with respect to t₂ to generate the transformeddata set S_(c) (t₁, F₂) or S₂ (t₁, F₂);

(e) obtaining phase angles θ₂ for phase shifting interferograms definedby t₁ values corresponding to selected F₂ values in the data sets S_(c)(t₁, F₂) or S_(s) (t₁, F₂) so that each peak in the interferogramscorresponding to peaks in the spectrums S_(c) (t₁₀₀₀, F₂) and S_(s)(t₁₀₀₀, F₂) takes an absorption or dispersion waveform;

(f) shifting the phases of all the data in data sets S_(c) (T₁, F₂) orS_(s) (t₁, F₂)derived in the step (d) by phase angles θ₂ to make phasecorrection; and

(g) shifting the phases of all the data in data sets S_(c) (t₁, F₂) orS_(s) (t₁, F₂) derived in the step (f) by phase angles θ₁ to make phasecorrection with respect to t₁, and simultaneously take the Fouriertransform of the data sets S_(c) (t₂, F₂) or S_(s) (t₁, F₂) with respectto t₁.

This spectrometry is characterized in that the phase of the dataobtained by the measurements are corrected immediately after it issubjected to Fourier transformation with respect to t₂.

Other objects and features of the invention will appear in the course ofthe description that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a sequence of measurements used for aJ-resolved two-dimensional nuclear magnetic resonance spectrometry;

FIG. 2 is a block diagram of a nuclear magnetic resonance spectrometerfor carrying out the present invention;

FIGS. 3(a) and 3(b) are a timing diagram for illustrating the operationof the spectrometer shown in FIG. 2;

FIG. 4 is a representation for illustrating the set S(t₁, t₂) of freeinduction decay signals;

FIGS. 5(a) and (b) are representations for illustrating S_(c) (t₁, F₂)and S_(s) (t₁, F₂), respectively;

FIGS. 6(a)-(b') are diagrams showing iterferograms;

FIGS. 7(a)-(b") are waveform diagrams for illustrating S_(c) (t₁₀₀₀, F₂)and S_(s) (t₁₀₀₀, F₂); and

FIGS. 8(a)-8(c) are diagrams for illustrating phase.

PREFERRED EMBODIMENT OF THE INVENTION

Referring to FIG. 2, there is shown a nuclear magnetic resonancespectrometer for carrying out the present invention. This spectrometerincludes a magnet 1 that produces a static magnetic field in which atransmitter/receiver coil 2 is placed. A sample to be investigated isinserted in the space inside the coil 2. An RF oscillator 3 generates aradio-frequency signal that contains the resonance frequency of thenuclei under investigation. This RF signal is supplied to the coil 2 asRF pulses via an amplifier 4 and agate 5, and then it is applied to thesample. As a result, a resonance signal is induced in the coil 2 and fedto a demodulator circuit 8 via a gate 6 and a receiver circuit 7. Thedemodulator circuit 8 also receives the RF signal as a reference signalfrom the RF oscillator 3. The free induction decay signal obtained fromthe demodulator circuit 8 is converted into digital form by ananalog-to-digital converter 9, and then it is furnished to a computer 10so that it is stored in a memory 11 incorporated in the computer.Thereafter, the data is arithmetically processed, i.e., it is subjectedto Fourier transformation, and the phases are corrected. The gates 5, 6,and the A/D converter 9 are controlled by a pulse programmer 12, whichhas been already programmed with the sequence of pulse trains applied tothe sample, pulse durations, and the timing of the sampling of dataperformed by the A/D converter 9. A sequence of measurement is madeaccording to the program.

Measurements are made in the sequence shown in FIG. 1 using theinstrument shown in FIG. 2 in the manner described below. The gate 5 isenabled during the periods shown in FIG. 3(a), so that a 90° pulse and a180° pulse are fed to the coil 2 at interval t₁ /2 and applied to thesample. After period t₁ /2 elapses since this application of the pulsetrain, the gate 6 is enabled during the period shown in FIG. 3(b). Atthe same time, the A/D converter 9 is caused to operate. Thus, theresulting free induction decay signal is detected during period t₂ andstored in the memory 11.

This single measurement is repeated with 256 different values of t₁. Forexample, t₁ assumes values t₁₀₀₀, t₁₀₀₁, t₁₀₀₂, t₁₀₀₃, . . . , t₁₂₅₅ inturn. Upon completion of the 256 measurements, the free induction decaysignals FID₀₀₀ -FID₂₅₅ which are obtained corresponding to the 256different values of t₁ are stored in the memory 11. The 256 differentfree induction decay signals stored in the memory 11 can be consideredto be the set S(t₁, t₂) of values t₁₀₀₀ (initial value), t₁₀₀₁, t₁₀₀₂,t₁₀₀₃, . . . , t₁₂₅₅ which are arranged corresponding to the values oft₁, as shown in FIG. 4.

We first take the Fourier transform of this set with respect to t₂ toconvert t₂ into frequency domain F₂, resulting in cosine component S_(c)(t₁, F₂) and sine component S_(s) (t₁, F₂). Both are further convertedinto frequency domain F₁ with respect to t₁ by Fourier transformation,resulting in four Fourier components S_(cc) (F₁, F₂), S_(ss) (F₁, F₂),S_(cs) (F₁, F₂) and S_(sc) (F₁, F₂). Then, two-dimensional spectrumS(F₁, F₂) is given by

    S(F.sub.1, F.sub.2)=S.sub.cc (F.sub.1, F.sub.2)-S.sub.ss (F.sub.1, F.sub.2)+S.sub.cs (F.sub.1, F.sub.2)-S.sub.sc (F.sub.1, F.sub.2) (1) ps

In the past, the power spectrum of this two-dimensional spectrum hasbeen given by

    |{S(F.sub.1, F.sub.2)}|.sup.2 =[(S.sub.cc (F.sub.1, F.sub.2)).sup.2 +(S.sub.ss (F.sub.1, F.sub.2)).sup.2 +(S.sub.cs (F.sub.1, F.sub.2)).sup.2 +(S.sub.sc (F.sub.1, 2)).sup.2 ].sup.1/2  (2)

This has presented the aforementioned problems.

The cosine component S_(c) (t₁, F₂) and the sine component S_(s) (t₁,F₂) obtained by the Fourier transformation with respect to t₂ describedabove are now discussed. FIGS. 5(a) and (b) show the cosine componentS_(c) (t₁, F₂) and the sine component S_(s) (t₁, F₂), respectively,which are expressed corresponding to FIG. 4. Because of the relationbetween the sine and cosine components, the peaks P appearing in FIGS.5(a) and (b) are 90° out of phase with each other. The Fourier transformof S_(c) (t₁, F₂) and S_(s) (t₁, F₂) with respect to t₁ means theFourier transform of the interferograms shown in FIGS. 6(a) and (b) withrespect to all the values of F₂. These interferograms shown in FIGS.6(a) and (b) are the sets of points having the same value of F₂ whichare taken in the direction indicated by the arrow A in FIG. 5(a), forexample. Let us take an example in which F₂ assumes value F_(2n). Oneinterferogram is given by connecting points S_(c) (t₁₀₀₀, F_(2n)), S_(c)(t₁₀₀₁, F_(2n)), S_(c) (t₁₀₀₂, F_(2n)), and so on which are indicated bydots in FIG. 5(a). The other interferogram is given by connecting pointsS_(s) (t₁₀₀₀, F_(2n)), S_(s) (t₁₀₀₁, F_(2n)), S_(s) (t₁₀₀₂, F_(2n)), andso on which are indicated by dots in FIG. 5(b).

In taking the Fourier transform of an interferogram, if the phase at theinitial value (the origin in time) is zero, and if it assumes a cosinewaveform (FIG. 6(a')) or a sine waveform (FIG. 6(b')), then no phaseshift will be introduced into the resulting Fourier transform. However,phase shifts can be seen at the points S_(c) (t₁₀₀₀, F_(2n)) and S_(s)(t₁₀₀₀, F_(2n)) of the interferograms shown in FIGS. 6(a) and (b) whichare taken at the initial value t₁₀₀₀. Accordingly, if the data issubjected to Fourier transformation as it is, a phase shift will appearin the resulting two-dimensional spectrum.

According to the present invention, firstly, the initial data S_(c)(t₁₀₀₀, F₂ ) or S_(s) (t₁₀₀₀, F₂) is obtained from S_(c) (t₁, F₂) orS_(s) (t₁, F₂) by inserting an initial value t₁₀₀₀. Waveform of theinitial data S_(c) (t₁₀₀₀, F₂) or S_(s))t₁₀₀₀, F₂) is observed withshifting the phase of t₂ in the initial data. The phase angle θ₂ forphase correction is determined in such a way that waveform of theinitial data S_(c) (t₁₀₀₀, F₂) or S_(s) (t₁₀₀₀, F₂) takes an absorptionor dispersion waveform.

These steps are explained in our specification accompanying with FIGS.7(a), (b), (a'), (b'), (a"), (b") and FIG. 8.

The initial data S_(c) (t₁₀₀₀, F₂) or S_(s) (t₁₀₀₀, F₂) or S_(s) (t₁₀₀₀,F₂) phase corrected by θ₂ is used for the following Fouriertransformation. Similarly, the phases of the other data in S_(c) (t₁,F₂) or S_(s) (t₁, F₂) are shifted also by θ₂ for phase correction.

The corrected data S_(c) (t₁, F₂) or S_(s) (t₁, F₂) is subjected toFourier transformation with respect to t₁, and simultaneously subjectedto phase correction with respect to t₁.

This step is explained in our specification accompanying with FIGS.6(a), (b), (a'), (b').

FIGS. 7(a) and (b) show waveform obtained from the data S_(c) (t₁₀₀₀,F₂) and the data S_(s) (t₁₀₀₀, F₂), respectively. The data S_(c) (t₁₀₀₀,F₂) is derived from S_(c) (t₁, F₂) by setting the initial value equal tot₁₀₀₀, while the data S_(s) (t₁₀₀₀, F₂) is derived from S_(s) (t₁, F₂)be setting the initial value equal to t₁₀₀₀. The peaks P appearing inthe waveforms shown in FIGS. 7(a) and (b) may be considered to be theprojection of a coil L consisting of a single turn as shown in FIG. 8(a)onto orthogonal X and Y planes, for facilitating the understanding.Specifically, if the orbit of gyromagnetic resonators near resonancepoint F_(2n) is given by the coil L in a three-dimensional manner, thenthe projection of this orbit onto the X plane is the waveform shown inFIG. 7(a). The projection of the orbit onto the Y plane is the waveformshown in FIG. 7(b). It is to be noted that the coil L is not shown inFIG. 8(b) but in reality the straight portion of the coil L conincideswith the axis Z. The relation of the coil L to the X and Y planescorresponds to phase. If the X and Y planes are rotated about the axis Zin FIG. 8(c), the relation of the coil L to the X and Y planes, orphase, changes. Thus the waveforms shown in FIGS. 7(a) and (b) change tothe waveforms shown in FIGS. 7(a') and (b'), respectively. Just whenthey rotate through a certain angle θ, the waveforms become theabsorption waveform shown in FIG. 7(a") and the dispersion waveformshown in FIG. 7(b"). This is the condition in which the initial phase iszero.

In order to shape the peaks P into such a waveform, the data S_(c)(t₁₀₀₀, F₂) and the data S_(s) (t₁₀₀₀, F₂) are given by cos ω and sin ω,respectively. Then, the waveforms are rotated through θ to derive cos(ω+θ) and sin (ω+θ). Obviously, these are arithmetically obtained fromthe equality cos (ω+θ)=cos ω cos θ- sin ω sin θ and the equality sin(ω+θ)=sin ω cos θ+cos ω sin θ.

In actuality, an arithmetic operation is repeated with different valuesof θ to find the value of θ₂ at which the peak intensity of anabsorption waveform takes on a maximum value. In this way, theabsorption and dispersion waveforms shown in FIGS. 7(a") and (b"),respectively, are provided. Let S_(c) (t₁₀₀₀, F₂) and S_(s) (t₁₀₀₀, F₂)be the corrected data.

In this manner, the phase angle θ₂ by which the phase is shifted forphase correction is found. And then, all the other data items containedin S_(c) (t₁, F₂) and S_(s) (t₁, F₂) are arithmetrically treated forphase correction to obtain Fourier components S_(c) (t₁, F₂) and S_(s)(t₁, F₂) the phases of which have been corrected with respect to t₂.

Further, the above Fourier components S_(c) (t₁, F₂) and S_(s) (t₁ , F₂)are arithmetrically treated for phase correction with phase angle θ₁ toobtain Fourier components S_(c) (t₁, F₂) and S_(s) (t₁, F₂) the phasesof which have been corrected with respect to t₁. Phase angle θ₁ in thephase correction is determined so that the interferograms as similarlyshown by FIG. 6(a) or FIG. 6(b) change the cosine waveform (FIG. 6(a))or sine waveform (FIG. 6(b)) by phase correction with respect to t₁. Inthis case, the interferogram as similarly shown by FIG. 6(a) or FIG.6(b) are obtained for the Fourier component S_(c) (t₁, F₂) and S_(s)(t₁, F₂) the phases of which have been corrected with respect to t₂.Then the Fourier components S_(c) (t₁, F₂) and S_(s) (t₁, F₂) aresubjected to Fourier transform with respect to t₁, so that thetwo-dimensional spectrum is derived. This two-dimensional spectrum isfree of phase shift and hence it is a correct spectrum.

Actually, the above phase correction and Fourier transform issimultaneously carried out by using the technique, for example,so-called "Fourier self-deconvolution method" as mentioned in Anal.Chem. 1981, 53, 1454-1457 or in APPLIED OPTICS, Vol. 20, No. 10, May 15,1981.

Additionally, it suffices to take the Fourier transform of only one ofS_(c) (t₁, F₂) and S_(s) (t₁, F₂). Therefore, the data which should beobtained after the phase correction is either S_(c) (t₁, F₂) or S_(s)(t₁, F₂).

Although the phases of all the data items have been corrected in thedescription thus far made, this is not essential to the presentinvention. For example, it is possible to correct only the data aboutthe range of F₂ in which a peak exists, by arithmetic operation. Where aplurality of peaks exist, correction may be made to the data about theranges of data in which the peaks exist. In this case, the phase anglethrough which phase is shifted for phase correction may differ from peakto peak. Accordingly, it is desired to make the phase angle differentamong the peaks.

I claim:
 1. A method of two-dimensional nuclear magnetic resonancespectrometry comprising the steps of:(a) applying a radio-frequencypulse train to a sample containing gyromagnetic resonators, the pulsetrain consisting of a plurality of radio-frequency pulses; (b) detectingthe free induction decay after the end of the application of theradio-frequency pulse train and storing it in a memory; (c) repeatingthe steps (a) and (b) with different values of evolution period t₁ thatis defined as the pulse separation between certain two pulses of theradio-frequency pulse train to generate the data set S(t₁, t₂) of thefree induction decay signals, the initial value of t₁ being identifiedas t₁₀₀₀ ; (d) taking the Fourier transform of the set S(t₁, t₂) of thefree induction decay signals with respect to t₂ to generate thetransformed data set S_(c) (t₁, F₂) or S_(s) (t₁, F₂); (e) obtainingphase angle θ₂ for phase shifting interferograms defined by t₁ valuescorresponding to selected F₂ values in the data sets S_(c) (t₁, F₂) orS_(s) (t₁, F₂) so that each peak in the interferograms corresponding topeaks in the spectrums S_(c) (t₁₀₀₀, F₂) and S_(s) (t₁₀₀₀, F₂) takes anabsorption or dispersion waveform; (f) shifting the phases of all thedata in data sets S_(c) (t₁, F₂) or S₂ (t₁, F₂) derived in the step (d)by phase angles θ₂ to make phase correction; and (g) shifting the phasesof all the data in data sets S_(c) (t₁, F₂) or S_(s) (t₁, F₂) derived inthe step (f) by phase angles θ₁ to make phase correction with respect tot₁, and then taking the Fourier transform of the data sets S_(c) (t₁,F₂) or S_(s) (t₁, F₂) with respect to t₁.